Make the puree: Toss the peach chunks and sugar in a small saucepan. Add the lime juice and chile, cover and cook over medium heat until the peaches are soft, stirring often, about 10 minutes. Remove the chile.

Mash the peaches with a vegetable masher or fork until smooth. Strain and let cool. The puree will keep in the refrigerator for up to 3 days, but is best used immediately.